Of course, the wallet is a separate entity, but it’s functionality is derived from your connection to the chain via your node. It won’t load without an instance of zcashd running.
…and you’re correct. Mining Zcash using EWBF, Claymore, et al does not constitute running a node, as those machines do not have their own local copy of the ledger that is available for comparison on the network.
To put it simply… you are competing with t1fJuHWrfcWnYMYyP9VAF96vRnvND2NziMG this guy… you can calculate the odds of finding a block before him… and even this guy is on a pool not mining solo… 
Try the testnet if you want to mine something solo with your CPU and see the message (if I recall it just says you’ve found a block or something like that). I’m not sure what the testnet difficulty is right now but it shouldn’t be too bad.
Add testnet=1 and addnode=testnet.z.cash to your ~/.zcash/zcash.conf file.
You could also run a miner and join a pool eg flypool etc to get a feel for hash rates etc
I’m like you and playing around
started with a full eth node (devnet at first then the main one but no chance of hitting anything) and am currently looking at zec from flypool, and getting 0.000x a day from my oldish gpu, but its a good learning experience
Update - I might have a play with that full zcash4win full node
How much disk space does it need for the ‘ledger’ ?
update2 - indicates it needs 10GB or so
There is absolutely nothing wrong with testing and learning. That’s how a lot of us start. The problem is people come here under the guise of testing and learning but what they really want is for someone to give them specific instructions on how to set up a rig that will make them thousands of dollars a day
How does one run ZCash4Win in “Full Node” mode? I’m thinking I need to run in “Full Nerd” mode to do it, so that is going, but I don’t know how to do Full Node with the wallet. Tx for any help!
It does it on it’s own. You don’t have to do anything to it. The wallet connects to the node that’s run in the background by the program itself. When you run the wallet, it runs the node. So if you want a node connected all the time, just leave the wallet running 
Easy! TY I’d think that by extension, then, that if I ran wallets on all of my miners that I’d create nine more new nodes. Is this correct?
Yes. However, keep in mind that if your Internet connection goes down for example, that would be 10 nodes wiped out until it returns. So while it seems like you’re doing a good thing, it’s actually the opposite.